Question

Is the number of homomorphisms between two isomorphic groups equals to the number of Automorphisms for each group?

score 132 · Answer 1 · 2022-12-08 11:00:54

132

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Is the number of homomorphisms between two isomorphic groups equals to the number of Automorphisms for each group?

Published on 08 Dec 2022 - 11:00

score 53 · Answer 2 · 2026-02-23 07:25:12

53

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Conjecture: if $H$ is characteristic in $G$ and $K\leq G$ such that $K\cong H$, then $H=K$.

Published on 23 Feb 2026 - 7:25

score 131 · Answer 3 · 2026-03-29 16:33:06

131

Views

Is this function an automorphism?

Published on 29 Mar 2026 - 16:33

score 72 · Answer 4 · 2022-12-14 19:21:47

72

Views

Combine the results of Exercises 45 and 47 into a single “if and only if” theorem.

Published on 14 Dec 2022 - 19:21

score 53 · Answer 5 · 2022-12-22 21:40:32

53

Views

Given a group $G$ and $N\unlhd G$ with $|N| = 3$ which is not contained in the center of $G$. Show that $G$ contains a subgroup $H$ with $[G:H] = 2$

Published on 22 Dec 2022 - 21:40

score 87 · Answer 6 · 2026-03-28 12:32:09

87

Views

Group satisfying the maximal (minimal) condition for normal subgroups but not satisfying the maximal (minimal) condition

Published on 28 Mar 2026 - 12:32

score 71 · Answer 7 · 2022-12-31 04:42:13

71

Views

Automorphism group of endomorphism monoid of an Abelian group

Published on 31 Dec 2022 - 4:42

score 116 · Answer 8 · 2023-01-02 18:25:12

116

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Fixed field of an automorphism group is Galois

Published on 02 Jan 2023 - 18:25

score 38 · Answer 9 · 2026-03-26 17:36:54

38

Views

Truncation of a Cayley graph

Published on 26 Mar 2026 - 17:36

score 84 · Answer 10 · 2023-01-05 06:09:51

84

Views

Does every Boolean algebra have an automorphism with exactly zero and one as fixed points?

Published on 05 Jan 2023 - 6:09

score 78 · Answer 11 · 2023-01-07 11:16:57

78

Views

Does the functor $\mathrm{Aut}$ have an adjoint

Published on 07 Jan 2023 - 11:16

score 75 · Answer 12 · 2023-01-14 10:38:34

75

Views

Equivalence of categories preserve automorphism group

Published on 14 Jan 2023 - 10:38

score 181 · Answer 13 · 2026-04-01 13:32:25

181

Views

Is $\text{PSL}_2(\mathbb{R})$ the automorphism group of the upper half plane?

Published on 01 Apr 2026 - 13:32

score 65 · Answer 14 · 2023-01-19 04:24:16

65

Views

Why this corollary force ${\rm Aut}(H)=1$, where $H$ isomorphic to $\Bbb Z_2$

Published on 19 Jan 2023 - 4:24

score 134 · Answer 15 · 2023-01-28 15:13:17

134

Views

Determine the Automorphism group of the quaternion group.

Published on 28 Jan 2023 - 15:13

List Question

Is the number of homomorphisms between two isomorphic groups equals to the number of Automorphisms for each group?

Conjecture: if $H$ is characteristic in $G$ and $K\leq G$ such that $K\cong H$, then $H=K$.

Is this function an automorphism?

Combine the results of Exercises 45 and 47 into a single “if and only if” theorem.

Given a group $G$ and $N\unlhd G$ with $|N| = 3$ which is not contained in the center of $G$. Show that $G$ contains a subgroup $H$ with $[G:H] = 2$

Group satisfying the maximal (minimal) condition for normal subgroups but not satisfying the maximal (minimal) condition

Automorphism group of endomorphism monoid of an Abelian group

Fixed field of an automorphism group is Galois

Truncation of a Cayley graph

Does every Boolean algebra have an automorphism with exactly zero and one as fixed points?

Does the functor $\mathrm{Aut}$ have an adjoint

Equivalence of categories preserve automorphism group

Is $\text{PSL}_2(\mathbb{R})$ the automorphism group of the upper half plane?

Why this corollary force ${\rm Aut}(H)=1$, where $H$ isomorphic to $\Bbb Z_2$

Determine the Automorphism group of the quaternion group.

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